(625e) Effects of Convective Flow and Extracellular Inhibitors On EGFR Signaling – Mathematical Modeling

We study effects of convective flow on velocity of signal transmission in epithelial tissue. It has been found that the convective transport is necessary in many developmental processes such as vascular and lymphatic system formation. Here, we focus on a one-layer epithelium system. We consider positive feedback loop ligand transport -> ligand-receptor binding -> intracellular processing -> ligand release. When a combination of diffusion and convective transport is considered in the extracellular space, we can see different regimes of ligand propagation or withdrawal at the epithelium. Parametrical studies dealing with effects of strength of ligand-receptor binding, geometric parameters, importance of ligand-receptor endocytosis or relative strength of ligand formation on signal propagation will be shown. We have developed three mathematical models that differ according to flow character above the epithelium: (i) plug flow along the epithelium, (ii) simplified plug flow model that exploits the thin fin approximation, (iii) laminar flow along the epithelium. We also found exact solutions of the models (i) and (ii) in asymptotic cases. All models were analyzed numerically (Comsol). When results of these models were compared, we realized that the simplified model (ii), which is spatially one-dimensional, describes behavior of the system with sufficient precision in most of physically relevant regimes. Hence, comprehensive continuation analysis of the model was carried out (AUTO07). The achieved results will be presented.

     Further, we extended the model for inhibition of EGFR signaling by extracellular inhibitors. The work was motivated by problems related to glioblastoma treatment. There is a blood-brain barrier that surrounds blood capillaries in brain. It often makes impossible to delivery chemotherapeutics in tumor. Now, convection enhanced transport delivery of therapeutics can be used in treatment. Here, we consider constant flux of EGFR inhibitor (EGFR antibodies) through the barrier to astrocyte tumor. Effects of intensity of inhibitor flux and oriented convection transport will be presented.